Does anyone know of similar libraries for Java that would work nicely with jME?
Having never heard about FFT water simulations before, I don't know what specific functionality in such a library you are looking for.
But of course there are a number of good math libraries available, http://commons.apache.org/math/ is but one of them.
Or is it fairly easy to tie into C++ libraries from jME?
The question should be "Or is it fairly easy to tie into C++ libraries from java?" - and the answer is, it is doable in a reasonable amount of time if you are familiar with the JNI (java native interface), the library you are trying to interface to, and c coding. Optionally you can try a wrapper generator like SWIG, but IMO that would not really be worth the effort for a small, specific subset of a math lib.
Yeah, good idea. I was dreaming that ODE would include something like this already but no luck.
But, hey! ode.org is back up and running! Last few days it was dead.
I actually also discovered that one of the fastest FFT implementations, FFTW (Fastest Fourier Transform in the West, believe it or not) actually has some java bindings ready to go. Very cool. Java may work out after all.